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Coloring numbers

Source: St Petersburg Olympiad 2014, Grade 11, P3

October 24, 2017
number theorycombinatoricsalgebrainequalities

Problem Statement

NN in natural. There are natural numbers from N3N^3 to N3+NN^3+N on the board. aa numbers was colored in red, bb numbers was colored in blue. Sum of red numbers in divisible by sum of blue numbers. Prove, that b∣ab|a
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